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  • I need help with Which of the following integral is not equal to the other integrals ?

Which of the following integral is not equal to the other integrals ?

  • Option 1)

    \int_{a}^{b}f(x)dx

  • Option 2)

    - \int_{b}^{a}f(y)dy

  • Option 3)

    \int_{b}^{a}f(t)dt

  • Option 4)

    \int_{a}^{b}f(z)dz

 

Answers (1)

best_answer

As we have learnt,

 

Fundamental Properties of Definite integration -

Interchanging the limit of the definite integral does not change the absolute value but change the sign of the integral.

\int_{a}^{b}f\left ( x \right )dx=- \int_{b}^{a}f\left ( x \right )dx

- wherein

         

 

 

 \int_{a}^{b}f(t)dt = -\int_{b}^{a}f(x)dx

So this integral is the odd one out.

 


Option 1)

\int_{a}^{b}f(x)dx

Option 2)

- \int_{b}^{a}f(y)dy

Option 3)

\int_{b}^{a}f(t)dt

Option 4)

\int_{a}^{b}f(z)dz

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gaurav

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